The British advanced in two columns. At this instant, the cannonade was brisk on both sides ; directed by the British across the hollow and Bronx, against the Americans on the hill, and by them returned. Almost at the same instant, the right column, composed of British troops, preceded by about twenty light horse in full gallop, and brandishing their swords, appeared on the road leading to the court-house, and now directly in the front of our General's division. The light-horse leaped the fence of a wheat field, at the foot of the hill, on which Col. Malcolm's regiment was posted, of which the light-horse were not aware until a shot from Lieut. Fenno's field-piece gave them notice by striking in the midst of them, and a horseman pitching from his horse. They then wheeled short about, galloped out of the field as fast as they came in, rode behind a little hill on the road, and faced about ; the tops of their caps only being visible to our General, where he stood. The column came no further up the road, but wheeled to I he left by platoons, as they came up ; and, passing through a bar, or gateway, directed their head towards the troops on Chatterton's hill, now engaged. When the head of the column had got nearly across the lot, their front got out of sight ; nor could the extent of their rear be now discovered. The sun shone bright, their arms glittered, and perhaps troops never were shown to more advantage, than these now appeared. The whole now halted ; and for a few minutes, the men all sat down in the same order in which they stood, no one appearing to move out of his place. The cannonade continued brisk across the Bronx.